7 chapter10

Chapter 10

Functional Dependencies andFunctional Dependencies and Normalization for Relational DatabasesDatabases

Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe

Chapter OutlineChapter Outline

Informal Design Guidelines for RelationalInformal Design Guidelines for Relational DatabasesFunctional Dependencies (FDs)p ( )Normalization of Relations and Different Normal Forms


Informal Design Guidelines for Relational Databases (1)Databases (1)

What is relational database design?What is relational database design?The grouping of attributes to form "good" relation schemas

Two levels of relation schemasThe logical "user view" levelgThe storage "base relation" level

Design is concerned mainly with base relationsg yWhat are the criteria for "good" base relations?


Informal Design Guidelines for Relational Databases (2)Databases (2)

We first discuss informal guidelines for goodWe first discuss informal guidelines for good relational designThen we discuss formal concepts of functional pdependencies and normal forms

- 1NF (First Normal Form)- 2NF (Second Normal Form)- 3NF (Third Normal Form)- BCNF (Boyce-Codd Normal Form)


Semantics of the Relation AttributesSemantics of the Relation Attributes

GUIDELINE 1: Informally, each tuple in a relation should y, prepresent one entity or relationship instance. Attributes of different entities (EMPLOYEEs, DEPARTMENT PROJECT ) h ld t b i d i thDEPARTMENTs, PROJECTs) should not be mixed in the same relation

Only foreign keys should be used to refer to other entitiesy g yEntity and relationship attributes should be kept apart as much as possible.

Bottom Line Design a schema that can be e plainedBottom Line: Design a schema that can be explained easily relation by relation. The semantics of attributes should be easy to interpret.


A simplified COMPANY relational database schemadatabase schema


Redundant Information in Tuples and Update AnomaliesUpdate Anomalies

Redundant Information causes:Redundant Information causes: storage wastageproblems with update anomaliesproblems with update anomalies

Insertion anomaliesDeletion anomaliesModification anomalies


Two relation schemas suffering from storage wastage and update anomaliesstorage wastage and update anomalies


Example States for EMP_DEPT and EMP PROJEMP_PROJ


EXAMPLE OF AN UPDATE ANOMALYEXAMPLE OF AN UPDATE ANOMALY

Consider the relation:Consider the relation:EMP_PROJ(Emp#, Proj#, Ename, Pname, No_hours))

Update Anomaly:Changing the name of project number P1 from g g p j“Billing” to “Customer-Accounting” may cause this update to be made for all 100 employees working on project P1on project P1.


EXAMPLE OF AN INSERT ANOMALYEXAMPLE OF AN INSERT ANOMALY


Insert Anomaly:Cannot insert a project unless an employee is p j p yassigned to it.

ConverselyCannot insert an employee unless he/she is assigned to a project.


EXAMPLE OF AN DELETE ANOMALYEXAMPLE OF AN DELETE ANOMALY


Delete Anomaly:When a project is deleted, it will result in deleting p j gall the employees who work on that project.Alternately, if an employee is the sole employee

j t d l ti th t l ld lt ion a project, deleting that employee would result in deleting the corresponding project.


Guideline to Redundant Information in Tuples and Update AnomaliesTuples and Update Anomalies

GUIDELINE 2:GUIDELINE 2: Design a schema that does not suffer from the insertion, deletion and update anomalies.If there are any anomalies present, then note them so that applications can be made to take them into

taccount.


Null Values in TuplesNull Values in Tuples

GUIDELINE 3:Relations should be designed such that their tuples will have as few NULL values as possibleAtt ib t th t NULL f tl ld b l d iAttributes that are NULL frequently could be placed in separate relations (with the primary key)

Nulls are problematic in joins and aggregate functionsp j gg gMany interpretations for nulls:

Attribute not applicable or invalidAttribute value unknown (may exist)Value known to exist, but unavailable


Spurious TuplesSpurious Tuples

Bad designs for a relational database may resultBad designs for a relational database may result in erroneous results for certain JOIN operations

GUIDELINE 4:Design relation schemas so that they can beDesign relation schemas so that they can be joined with equality conditions on attributes that are (primary key, foreign key) pairs in a way that

t th t i t l t dguarantees that no spurious tuples are generated.No spurious tuples should be generated by doing a natural join of any relations


a natural-join of any relations.

Functional Dependencies (1)Functional Dependencies (1)

Functional dependencies (FDs)Functional dependencies (FDs)Are constraints that are derived from the meaningand interrelationships of the data attributesAre used to specify formal measures of the "goodness" of relational designs

A set of attributes X functionally determines a set of attributes Y if the value of X determines a

i l f Yunique value for Y


Functional Dependencies (2)Functional Dependencies (2)X -> Y holds if whenever two tuples have the same value f X th t h th l f Yfor X, they must have the same value for Y

For any two tuples t1 and t2 in any relation instance r(R): If t1[X]=t2[X], then t1[Y]=t2[Y]

X Y i R ifi t i t ll l ti i tX -> Y in R specifies a constraint on all relation instances r(R)Written as X -> Y; can be displayed graphically on a

l ti h i Fi ( d t d b th )relation schema as in Figures. ( denoted by the arrow: ).FDs are derived from the real-world constraints on the attributes If K i k f R th K f ti ll d t i llIf K is a key of R, then K functionally determines all attributes in R

since we never have two distinct tuples with t1[K]=t2[K])


Examples of FD constraintsExamples of FD constraints

Social security number determines employee y p yname

SSN -> ENAMEProject number determines project name and location

PNUMBER > {PNAME PLOCATION}PNUMBER -> {PNAME, PLOCATION}Employee ssn and project number determines the hours per week that the employee works onthe hours per week that the employee works on the project

{SSN, PNUMBER} -> HOURS


Inference Rules for FDsInference Rules for FDsGiven a set of FDs F, we can infer additional FDs that hold whenever h FD i F h ldthe FDs in F hold

Armstrong's inference rules:IR1. (Reflexive) If Y subset-of X, then X -> YIR2. (Augmentation) If X -> Y, then XZ -> YZ

(Notation: XZ stands for X U Z)IR3. (Transitive) If X -> Y and Y -> Z, then X -> Z

Some additional inference rules that are useful:Decomposition: If X -> YZ, then X -> Y and X -> ZUnion: If X -> Y and X -> Z, then X -> YZPsuedotransitivity: If X -> Y and WY -> Z, then WX -> Z

The last three inference rules, as well as any other inference rules, can be deduced from IR1, IR2, and IR3 (completeness property)


Normalization of RelationsNormalization of RelationsNormalization:

The process of decomposing unsatisfactory "bad" relations by breaking up their attributes into smaller relations

Normal form:Condition using keys and FDs of a relation to certify whether a relation schema is in a particular normal form Normal form of a relation is the highest NF condition that it meets, and hence indicates the degree to which it has been normalizedand hence indicates the degree to which it has been normalized

2NF, 3NF, BCNF based on keys and FDs of a relation schema

4NF4NFbased on keys, multi-valued dependencies : MVDs

5NF b d k j i d d i JD


based on keys, join dependencies : JDs

Definitions of Keys and Attributes Participating in Keys (1)Participating in Keys (1)

A superkey of a relation schema R = {A1, A2, ....,A superkey of a relation schema R {A1, A2, ...., An} is a set of attributes S subset-of R with the property that no two tuples t1 and t2 in any legal relation state r of R will have t1[S] = t2[S]

A key K is a superkey with the additional property that removal of any attribute from K will

K b kcause K not to be a superkey any more.


Definitions of Keys and Attributes Participating in Keys (2)Participating in Keys (2)

If a relation schema has more than one key, eachIf a relation schema has more than one key, each is called a candidate key.

One of the candidate keys is arbitrarily designated y y gto be the primary key, and the others are called secondary keys.

A Prime attribute must be a member of somecandidate keyA N i tt ib t i t i tt ib tA Nonprime attribute is not a prime attribute—that is, it is not a member of any candidate key.


First Normal FormFirst Normal Form

DisallowsDisallowscomposite attributesmultivalued attributesmultivalued attributesnested relations; attributes whose values for an individual tuple are non-atomic

Considered to be part of the definition of relation p


Normalization into 1NFNormalization into 1NF


Normalization of nested relations into 1NFNormalization of nested relations into 1NF


Second Normal Form (1)Second Normal Form (1) Uses the concepts of FDs, primary keyp p y yDefinitions

Prime attribute: An attribute that is member of the primary key Kkey KFull functional dependency: a FD Y -> Z where removal of any attribute from Y means the FD does not hold any moremore

Examples:{SSN, PNUMBER} -> HOURS is a full FD since neither SSN > HOURS nor PNUMBER > HOURS hold-> HOURS nor PNUMBER -> HOURS hold

{SSN, PNUMBER} -> ENAME is not a full FD (it is called a partial dependency ) since SSN -> ENAME also holds


Second Normal Form (2)Second Normal Form (2)

A relation schema R is in second normal formA relation schema R is in second normal form (2NF) if every non-prime attribute A in R is fully functionally dependent on the primary key

R can be decomposed into 2NF relations via the pprocess of 2NF normalization


Normalizing into 2NFNormalizing into 2NF


Third Normal Form (1)Third Normal Form (1)

Definition:Transitive functional dependency: a FD X -> Z that can be derived from two FDs X -> Y and Y -> ZZ

Examples:SSN -> DMGRSSN is a transitive FDSSN -> DMGRSSN is a transitive FD

Since SSN -> DNUMBER and DNUMBER -> DMGRSSN hold

SSN -> ENAME is non-transitiveSince there is no set of attributes X where SSN -> X and X -> ENAME


and X > ENAME

Third Normal Form (2)Third Normal Form (2)A relation schema R is in third normal form (3NF) if it is ( )in 2NF and no non-prime attribute A in R is transitively dependent on the primary keyR can be decomposed into 3NF relations via the processR can be decomposed into 3NF relations via the process of 3NF normalization NOTE:

I X > Y d Y > Z ith X th i k idIn X -> Y and Y -> Z, with X as the primary key, we consider this a problem only if Y is not a candidate key.When Y is a candidate key, there is no problem with the t iti d dtransitive dependency .E.g., Consider EMP (SSN, Emp#, Salary ).

Here, SSN -> Emp# -> Salary and Emp# is a candidate key.


Normalizing into 3NFNormalizing into 3NF


Normal Forms Defined InformallyNormal Forms Defined Informally

1st normal form1 normal formAll attributes depend on the key

2nd normal form2 normal formAll attributes depend on the whole key

3rd normal form3 normal formAll attributes depend on nothing but the key


General Normal Form Definitions (1)General Normal Form Definitions (1)

The above definitions consider the primary keyThe above definitions consider the primary key onlyThe following more general definitions take into g gaccount relations with multiple candidate keysA relation schema R is in second normal form (2NF) if every non-prime attribute A in R is fully functionally dependent on every key of R


General Normal Form Definitions (2)General Normal Form Definitions (2)

Definition:Definition:Superkey of relation schema R - a set of attributes S of R that contains a key of RyA relation schema R is in third normal form (3NF)if whenever a FD X -> A holds in R, then either:

(a) X is a superkey of R, or (b) A is a prime attribute of R

NOTE B C dd l f di llNOTE: Boyce-Codd normal form disallows condition (b) above


Normalization into General 2NF and 3NFNormalization into General 2NF and 3NF


BCNF (Boyce Codd Normal Form)BCNF (Boyce-Codd Normal Form)

A relation schema R is in Boyce-Codd Normal Form y(BCNF) if whenever an FD X -> A holds in R, then X is a superkey of RE h l f i t i tl t th th iEach normal form is strictly stronger than the previous one

Every 2NF relation is in 1NFyEvery 3NF relation is in 2NFEvery BCNF relation is in 3NF

There exist relations that are in 3NF but not in BCNFThe goal is to have each relation in BCNF (or 3NF)


Boyce Codd normal formBoyce-Codd normal form


A relation TEACH that is in 3NF but not in BCNFBCNF

fd1: { student course} > instructorfd1: { student, course} -> instructorfd2: instructor -> course


Achieving the BCNF by DecompositionAchieving the BCNF by Decomposition

Two FDs exist in the relation TEACH:fd1: { student, course} -> instructorfd2: instructor -> course

{student, course} is a candidate key for this relation and that the dependencies shown follow the pattern in Figure 10 12 (b)the pattern in Figure 10.12 (b).

So this relation is in 3NF but not in BCNF A relation NOT in BCNF should be decomposedA relation NOT in BCNF should be decomposed so as to meet this property.

{instructor, course } and {instructor, student}


7 chapter10

Engineering